Could you explain more where this matrix equation came from and why we don't want to use the standard SVD?
motoole2
Sure! In the previous slide, we derived an overdetermined linear system $Ax = b$ between the flow vector, $x = [u,v]$, and our temporal gradients $b$. The equation here solves for the least squares solution by (1) multiplying both sides by $A^T$, and (2) inverting the 2x2 matrix $A^T A$ to solve for $x$.
Why don't we want to use the SVD here? We absolutely could. However, the solution is a little more efficient that computing the SVD. And we also use the form of $A^T A$ to explain the connection to the Harris corner detector a little later in this lecture.
Could you explain more where this matrix equation came from and why we don't want to use the standard SVD?
Sure! In the previous slide, we derived an overdetermined linear system $Ax = b$ between the flow vector, $x = [u,v]$, and our temporal gradients $b$. The equation here solves for the least squares solution by (1) multiplying both sides by $A^T$, and (2) inverting the 2x2 matrix $A^T A$ to solve for $x$.
Why don't we want to use the SVD here? We absolutely could. However, the solution is a little more efficient that computing the SVD. And we also use the form of $A^T A$ to explain the connection to the Harris corner detector a little later in this lecture.